Recommender systems are widely used. Usually, recommender systems are based on a centralized client-server architecture. However, this approach implies drawbacks regarding the privacy of users. In this paper, we propose a distributed reciprocal recommender system with strong, self-determined privacy guarantees, i.e., local differential privacy. More precisely, users randomize their profiles locally and exchange them via a peer-to-peer network. Recommendations are then computed and ranked locally by estimating similarities between profiles. We evaluate recommendation accuracy of a job recommender system and demonstrate that our method provides acceptable utility under strong privacy requirements.